Logic Masters Deutschland e.V.

The following puzzle goes back from one of my first desires when learning how to set puzzles in the first few weeks, that is setting a puzzle consisting of 4 small sudokus linked together by extra conditions. The idea on this puzzle is an experimental one and I'm still building some ideas for the bigger version (6x6) in free times at the moment, for now here's a 4x4 version of it.

The rule set is quite long but the bigger 6x6 version will pretty much have the same amount of rule like this one so solver should read them carefully first. I hope you enjoy the 4x4 version!

Rules:

- Normal Sudoku rules apply for each of 4x4 grid, each contains a set of 4 digits from the set of digits from 1-6 and solver needs to deduce which digits each grid has to contain.

- Variant applies for each grid:
+ Doubler: The 4 available gray cells are doublers. For the sake of evaluation, a doubler containing a digit has the value of that digit doubled. Each gray cell contains a unique digit.
+ Killer: Digits within a cage don't repeat and they sum to the small number written in the corner of that cage (if given). X is a positive integer that needs to be deduced.
+ Mathrax: Each circle contains a number and an arithmetic operator, where the number is the result when you apply that operation to both pairs of diagonally opposite cells (in this case: + is addition, / is division). ? is a number that needs to be deduced (not necessary an integer).
+ Little Killer Remainder: A numbered clue outside the grid shows the remainder when the sum of all cells along the diagonal is divided by the first cell along that diagonal (in this case, R3C4 of that grid).

- A square between two adjacent grids contains a thing that shows a relationship between two adjacent cells to it, including:
+ Adjacent cells contain digits with consecutive relationship - indicated as a white dot.
+ Adjacent cells contain digits with the 1:2 ratio relationship - indicated as a black dot.
+ Adjacent cells contain digits with the total of 5 - indicated as label V.
+ Adjacent cells contain digits with the total of 9 - indicated as label IX.

- A given hyphen (-) in the square shows that adjacent cells don't satisfy any of the above relationship. If a hyphen isn't given in a square, the square must be either one of the four above relationships.

- In a series of four consecutive squares, no two of them will contain the same thing, e.g. if one square contains a V, none of the rest in its series can contain another V. It's possible that two adjacent cells of a square satisfy multiple relationships above, e.g. 1 and 2 may have either white dot (consecutive) or black dot (1:2 ratio) between them.

Puzzle (no answer check): Penpa plus link

Good luck and have fun solving!